Rewrite as a simplified fraction. ${0.2\overline{63} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 263.6363...\\ 10x &= 2.6363...\end{align*}}$ Subtracting the two equations, we have: ${990x = 261}$ ${x = \dfrac{261}{990}} $ ${x = \dfrac{29}{110}} $